Research on calculus: what do we know and where do we need to go?

In this introductory paper we take partial stock of the current state of field on calculus research, exemplifying both the promise of research advances as well as the limitations. We identify four trends in the calculus research literature, starting with identifying misconceptions to investigations of the processes by which students learn particular concepts, evolving into classroom studies, and, more recently research on teacher knowledge, beliefs, and practices. These trends are related to a model for the cycle of research and development aimed at improving learning and teaching. We then make use of these four trends and the model for the cycle of research and development to highlight the contributions of the papers in this issue. We conclude with some reflections on the gaps in literature and what new areas of calculus research are needed.     

Identification of Intermediates in Zeolite‐Catalyzed Reactions by In Situ UV/Vis Microspectroscopy and a Complementary Set of Molecular Simulations

The optical absorption properties of (poly)aromatic hydrocarbons occluded in a nanoporous environment were investigated by theoretical and experimental methods. The carbonaceous species are an essential part of a working catalyst for the methanol‐to‐olefins (MTO) process. In situ UV/Vis microscopy measurements on methanol conversion over the acidic solid catalysts H‐SAPO‐34 and H‐SSZ‐13 revealed the growth of various broad absorption bands around 400, 480, and 580 nm. The cationic nature of the involved species was determined by interaction of ammonia with the methanol‐treated samples. To determine which organic species contribute to the various bands, a systematic series of aromatics was analyzed by means of time‐dependent density functional theory (TDDFT) calculations. Static gas‐phase simulations revealed the influence of structurally different hydrocarbons on the absorption spectra, whereas the influence of the zeolitic framework was examined by using supramolecular models within a quantum mechanics/molecular mechanics framework. To fully understand the origin of the main absorption peaks, a molecular dynamics (MD) study on the organic species trapped in the inorganic host was essential. During such simulation the flexibility is fully taken into account and the effect on the UV/Vis spectra is determined by performing TDDFT calculations on various snapshots of the MD run. This procedure allows an energy absorption scale to be provided and the various absorption bands determined from in situ UV/Vis spectra to be assigned to structurally different species.     

Design,synthesis, and application of chiral electron-poor guanidines as hydrogen-bonding catalysts for the Michael reaction

The first chiral electron-poor guanidine organocatalysts were synthesized. The presence of a tunable electron-withdrawing group on the guanidine moiety allows for the modulation of the catalysts’ activity. The application of this new class of organocatalysts to the Michael reaction is demonstrated.     

Determination of anthocyanins in the urine of patients with colorectal liver metastases after administration of bilberry extract

Anthocyanins possess cancer chemopreventive properties in preclinical models. Their clinical pharmacology is only poorly understood. In this pilot study, anthocyanins and their metabolites were analysed in the urine of two patients with colorectal liver metastases. They received a single dose of 1.88 g standardized bilberry extract (mirtoselect) via either nasogastric or nasojejunal tube intra‐operatively during liver resection. HPLC‐MS/MS and HPLC‐UV analysis showed there were more anthocyanins and metabolites in the urine of the patient who received mirtoselect via the stomach than via the jejunum. This result is consistent with information obtained in rodents which suggests the stomach is the predominant site for anthocyanin absorption. Copyright © 2010 John Wiley & Sons, Ltd.     

Multiscale Lagrangian fluid dynamics simulation for polymeric fluid

We have developed a simulation technique of multiscale Lagrangian fluid dynamics to tackle hierarchical problems relating to historical dependency of polymeric fluid. We investigate flow dynamics of dilute polymeric fluid by using the multiscale simulation approach incorporating Lagrangian particle fluid dynamics technique (the modified smoothed particle hydrodynamics) with stochastic coarse‐grained polymer simulators (the dumbbell model). We have confirmed that our approach is well in agreement with the macroscopic results obtained by a constitutive equation corresponding to the dumbbell model, and observed that microscopic thermal fluctuation appears in macroscopic fluid dynamics as dispersion phenomena. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 886–893, 2010     

An Interpenetrated Framework Material with Hysteretic CO2 Uptake

A new, twofold interpenetrated metal–organic framework (MOF) material has been synthesized that demonstrates dramatic steps in the adsorption and hysteresis in the desorption of CO₂. Measurement of the structure by powder X‐ray diffraction (PXRD) and pair distribution function (PDF) analysis indicates that structural changes upon CO₂ sorption most likely involve the interpenetrated frameworks moving with respect to each other.     

Multiplicity-Free Permutation Representations of the Symmetric Group

We determine all the multiplicity-free representations of the symmetric group. This project is motivated by a combinatorial problem involving systems of set-partitions with a specific pattern of intersection.